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TSGL: Teacher-Student Graph Learning for 3DGS Compression
Matin Bani Saedi, Matthew Kyan, Gene Cheung
TL;DR
3DGS models contain millions of richly attributed Gaussians, making them costly to store, while position-only graphs can miss attribute similarities. TSGL learns a signal-dependent graph from decoder-available inputs and applies GFT to remaining attributes. Across three benchmarks, it achieves 27×–33× compression with less than 0.6 dB PSNR degradation, improving on recent post-training methods.
Problem
Millions of richly attributed Gaussian primitives make 3DGS costly to store, and position-based graph weights may miss attribute differences between nearby primitives.
Source: §1 · p. 1Method
TSGL learns a student graph to mimic a teacher graph of signal geometry from decoded positions and DC SH coefficients, then applies GFT to remaining attributes.
Source: §1 · p. 1Results
27×–33× compression keeps PSNR degradation below 0.6 dB across three benchmarks while improving rate-distortion performance over recent post-training methods.
Source: §1 · p. 2Takeaways & Limitations
The student graph reproduces teacher graph information from decoder-available inputs, so the graph itself need not be transmitted.
Source: §6 · p. 4
Abstract
from arXiv · showhide
3D Gaussian Splatting (3DGS) is a popular representation for novel view synthesis. However, 3DGS contains millions of Gaussian primitives, each with rich attributes, resulting in large file sizes. We propose a novel 3DGS compression method based on Teacher-Student Graph Learning (TSGL) that operates directly on a trained model, without 3DGS retraining or access to training images. Specifically, for each block of Gaussian primitives, using decoded positions and DC spherical harmonic (SH) coefficients as predictors, we learn a signal-dependent geometry graph G encoding the pairwise similarities between neighbouring Gaussians via a teacher-student model. Given G, we perform Graph Fourier Transform (GFT) on the remaining attributes, so that signal energies are predominantly projected into the low-frequency coefficients for compact representation. On three standard benchmarks, the method reaches 27x to 33x compression with less than 0.6 dB of PSNR loss, improving on recent post-training compression methods in both size and rendering quality.
1. INTRODUCTION
3DGS is costly to store because it contains many richly attributed Gaussians, and position-only graphs can miss attribute differences between nearby primitives. TSGL learns a signal-dependent graph from decoder-available information and uses it for transform coding of the remaining attributes.
1. INTRODUCTION
- Position-based graph weights can be inadequate because nearby Gaussian primitives may have greatly differing attributes, limiting GFT energy compaction.The paper frames transform coding as its focus for 3DGS attribute compression.Source: §1 · p. 1
- TSGL learns a student graph to mimic a teacher encoding attribute geometry, using decoded positions and DC SH coefficients as predictors.The resulting graph is used for GFT of the remaining attributes, concentrating signal energy in low-frequency coefficients for compact representation.Source: §1 · p. 1
- Across 13 scenes from three standard benchmarks, the method achieves 27× to 33× compression while remaining within 0.6 dB of original models in PSNR, improving rate-distortion performance over recent post-training methods.Source: §1 · p. 2
2. PRELIMINARIES
A 3DGS primitive has geometric, opacity, and spherical-harmonic attributes. Graph signal processing represents node-linked values using a graph, while the GFT expresses those values in a basis derived from the graph Laplacian.
2.1. 3D Gaussian Splatting
- Each 3DGS primitive comprises position, opacity, rotation, scale, and a 48-dimensional spherical-harmonic coefficient vector.The SH vector has a DC component for base colour and AC components for view-dependent colour variation.Source: §2.1 · p. 2
2.2. Graph Signal Processing
- A graph signal assigns values to graph nodes, and its Laplacian is defined from the degree matrix and adjacency matrix.The Laplacian definition is given as L ≜ D − W.Source: §2.2 · p. 2
2.3. Graph Fourier Transform
- The GFT basis consists of the graph Laplacian's eigenvectors, ordered by eigenvalue, and the transform produces graph-frequency coefficients.The inverse transform reconstructs the signal from those coefficients.Source: §2.3 · p. 2
3. PROPOSED CODING FRAMEWORK
The framework prunes and partitions the scene, codes positions and DC SH coefficients, then uses graph-based transforms and entropy coding for the remaining attributes. A channel-wise KLT further decorrelates the transformed AC SH coefficients.
3.1. Pruning, Base Attribute Coding, and Spatial Partitioning
- The framework prunes low-opacity and low-importance primitives, codes positions and DC SH coefficients, then partitions primitives into decoder-reproducible KD-tree blocks.Blocks contain at most 200 primitives to limit the cost of graph-Laplacian eigendecomposition.Source: §3 · p. 2, §3.1 · p. 2
3.2. Transform Coding, Quantization, and Entropy Coding
- The GFT transforms AC SH coefficients, scale, opacity, and rotation along the primitive dimension; a channel-wise KLT decorrelates AC SH coefficients.The transformed coefficients are uniformly quantized and coded with a static rANS entropy coder.Source: §3.2 · pp. 2–3
- A channel-wise KLT basis is computed from AC SH covariance and applied along the channel dimension, while the GFT operates along the primitive dimension.The KLT basis is computed once per scene and transmitted as side information.Source: §3.2 · pp. 2–3
4. TEACHER-STUDENT GRAPH LEARNING
TSGL constructs a signal-dependent graph so GFT energy for each signal concentrates in low-frequency coefficients. A teacher graph built from true attributes guides a student that estimates signal geometry from decoder-available information.
4. TEACHER-STUDENT GRAPH LEARNING
- The signal-dependent graph is constructed for each individual signal to concentrate its energy in low-frequency GFT coefficients.Unlike aggregate statistical decorrelation by KLT, this graph encodes deterministic signal geometry.Source: §4 · p. 3
4.1. Candidate Set
- Each primitive’s candidate set combines its 16 nearest positional neighbours and 16 nearest DC-colour neighbours, both available at the decoder.The candidate edge set is fixed by this design rule.Source: §4.1 · p. 3
4.2. Teacher Graph
- The teacher graph uses true attributes to represent block signal geometry, assigning edge weights according to joint attribute differences.The student learns to estimate this attribute-informed target; attribute contributions are normalized by their total variances.Source: §4.2 · p. 3
4.3. Student Network
- A per-scene student estimates teacher signal geometry from decoder-available position and DC colour, then its scores are normalized over each primitive’s candidate set.The student is trained by cross-entropy to match the teacher; at decoding, the two score directions are averaged to form an undirected adjacency matrix whose Laplacian defines the GFT basis.Source: §4.3 · p. 3
5. EXPERIMENTS
Across three datasets, TSGL achieves 27× to 33× compression with average PSNR degradation below 0.6 dB. Experiments compare post-training methods under matched evaluation conditions and ablate the contributions of graph GFT and channel KLT.
5.1. Experimental Settings
- Evaluation covers 13 scenes from three datasets; competing methods use the same renderer, test views, and resolution where re-evaluated, with re-optimization disabled for the post-training comparison.FlexGaussian values are quoted from its original paper; reported sizes include the complete bitstream components.Source: §5.1 · p. 4
5.2. Experimental Results
- On Mip-NeRF 360, TSGL uses 29.32 MB versus MesonGS at 34.41 MB and improves PSNR by 0.29 dB; on Tanks and Temples, it is 6.4% smaller than EntropyGS.On Deep Blending, MesonGS has 0.06 dB higher PSNR but requires 7.97 MB more storage on average.Source: §5.2 · p. 4
- 27× to 33× smaller than original 3DGS, with average PSNR degradation below 0.6 dB on all three datasets.Source: §5.2 · p. 4
- Opacity and importance pruning, G-PCC, and DC-SH vector quantization reduce original model size by approximately 40–45% with negligible visual-quality impact.Adding learned-graph GFT reduces file size and improves PSNR across all three datasets; Table 2 reports the pipeline stages by dataset, with each row adding one stage.Source: §5.2 · p. 4, Table 2 · p. 4
- Channel KLT further improves PSNR by 0.35, 0.19, and 0.16 dB across Mip-NeRF 360, Tanks and Temples, and Deep Blending, respectively.It reduces bitstream size by 3.6% and 2.2% on the first two datasets, but costs 2.0% on Deep Blending.Source: §5.2 · p. 4
6. CONCLUSION
TSGL compresses 3DGS by learning a student network to reproduce a teacher graph from decoder-available inputs, allowing the GFT basis to reflect signal geometry without transmitting the graph. Experiments report better performance than recent post-training methods on most quality and size measurements across three benchmarks.
6. CONCLUSION
- TSGL outperforms recent post-training compression methods on most quality and size measurements across three standard benchmarks.Source: §6 · p. 4
- A small student network reproduces a teacher graph built from true attributes using only decoder-available inputs, so the graph need not be transmitted.Source: §6 · p. 4
- A scene-level channel-wise KLT is applied to AC SH coefficients to remove correlation across channels.Source: §6 · p. 4